Analysis of singularity of solutions to the Navier-Stokes equations

纳维-斯托克斯方程解的奇异性分析

• 批准号: 21740106
• 负责人: SUZUKI Tomoyuki
• 金额: $ 1.83万
• 依托单位: Kanagawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740106/
• 关键词: 偏微分方程式; 関数方程式論

We prove regularity of weak solutions to the Navier-Stokes equations under the conditions on the pressure. In particular, we exelude the possibility of blow-up in the case that the pressure is small enough in scaling invariant spaces based on Lorentz spaces. This result can be applied to MHD equations if the magnetic field in addition to the pressure belongs to the scaling invariant spaces based on the Lorentz spaces with small norms.

证明了在一定压力条件下Navier-Stokes方程弱解的正则性。特别地，我们排除了在基于洛伦兹空间的尺度不变空间中压力足够小的情况下爆炸的可能性。如果磁场和压力都属于基于小范数洛伦兹空间的尺度不变空间，则该结果可以应用于MHD方程。